When 15 newtons of force is applied to the 0.5 kg book, the friction keeps the book from sliding down the wall. What is the minimum force and minimum coefficent of frition to keep the book from sliding?

15 N and 3.061

Explanation:

From the question,

The minimum force of friction to keep the book from sliding = 15 N.

using

F = mgμ ... Equation 1

Where F = Frictional Force, m = mass of the book, g = acceleration due to gravity, μ = coefficient of friction.

make μ the subject of the equation

μ = F/mg ... Equation 2

Given: F = 15 N, m = 0.5 kg, g = 9.8 m/s²

Substitute into equation 2

μ = 15 (0.5*9.8)

μ = 15/4.9

μ = 3.061

Hence the coefficient of friction to keep the book from sliding = 3.061

Frictional force = 5N

Coefficient of friction = 0.33

Explanation;

Frictional force is a force of opposition acting in the opposite direction to the direction of the moving body. Since the body is acting against the wall, the body will move along the vertical in the direction of its weight. This means that the frictional force will act opposite the weight of the object.

To keep the body at rest, the sum of the forces along the horizontal and vertical component must be zero.

Sum of forces along the vertical will be Ff + (-W) = 0

Ff - W = 0

Ff = W where

Ff is the frictional force

W is the weight

Since W = mg, Ff = mg

Given the mass = 0.5kg

Ff = 0.5*10

Ff = 5N

The minimum force that wilk keep the book from sliding is 5N

According to the formula for calculating frictional force (Ff)

Ff = nR where;

n is the coefficient of friction

R is the normal reaction

The normal reaction is the force applied to the book in the horizontal direction.

Given R = 15N

n = Ff/R

n = 5/15

n = 0.33

The minimum coefficent of friction to keep the book from sliding is 0.33